**1. Introduction**

With the increasing demand of power and the gradually expanding scale of power grids, higher requirements have been placed on the power supply reliability of systems. In order to improve the reliability of power supply, it is one of the most important tasks to analyze the operational status of a distribution network, and evaluating the status of distribution equipment for the distribution network is an important part of the transmission and distribution of electric energy in a power system [1–3]. Testing the distribution transformers, circuit breakers and other power distribution equipment, and evaluating its operating status, can ensure the safety performance of the equipment and the reliability of the distribution network, and it is of grea<sup>t</sup> significance to ensure the safe and stable operation of the distribution network and improve the economics of the power supply enterprise.

Due to the wide distribution and large amount of distribution equipment, and the large amount of operational monitoring data without uniform evaluation standards, grea<sup>t</sup> di fficulties have been brought to the assessment of distribution equipment [4–10]. As one of the most important pieces of equipment of a distribution network, power transformers have also been paid much attention.

In response to the above problems, domestic and foreign experts have conducted a lot of research, and fuzzy evaluation, artificial intelligence and other methods are widely used in transformer state evaluation [11–15]. Reference [3] presents an evidential reasoning (ER) approach to the transformer condition assessment [3]. The methodology of transferring the transformer condition assessment problem into a multiple-attribute decision-making (MADM) solution under an ER framework is then presented in [3]. Based on the outputs of the ER approach, system operators can obtain an overall

evaluation of an observed unit's condition; also, several units may be ranked in order of severity for system maintenance purposes [3]. In [16] they used artificial neural networks to construct a multi-information fusion model to comprehensively evaluate transformer status. The validity of the method was verified by a case study. Based on the fuzzy theory, references [17–20] evaluated the operating state of the transformer, and verified the e ffectiveness of the evaluation method by example. However, no specific standard was given for the selection of the evaluation index. In reference [21], the transformer evaluation index function was established based on the semi-Cauxi distribution, and the transformer state evaluation model of multi-information fusion was established considering the di fference of the initial values of the indicators. In reference [22], an adaptive evolutionary limit learning machine algorithm is proposed, which was applied to the transformer state evaluation process, but the selection of transformer evaluation information needs to be optimized. In reference [23], based on the matter-element di fferential transformation, a transformer hierarchical evaluation model is established. At the same time, the concept of expert validity material element is introduced to make the weight determination more reasonable. In reference [24], based on DGA and SVM, the transformer state is evaluated, and the oil-immersed transformer is taken as an example for verification. Reference [25] introduces a transformer fleet monitoring solution to help the end user to group transformer assets and react accordingly to monitored situations [25]. Reference [26] establishes an index assessing system, considering the main body, the bushing and the accessories components, employs a Cauchy membership function for fuzzy grades division and represents a fuzzy evidence fusion method to handle the fuzzy evidence fusion processes [26]. In reference [27], a new multi-criterion based fuzzy logic model has been proposed to determine the overall health index of transformers. The method relies on the concentrations of individual dissolved gasses, significant diagnostic test results of transformer oil and paper insulation [27]. In reference [28], a novel method for DGA and FRA results unification is proposed, which is based on fuzzy sets application in failures detection and interpretation stages. In reference [29], a fuzzy logic technique for on-line condition diagnostics of transformer oil on the basis of leakage current flows through silica gel of breather and changes the color of silica gel [29].

The above evaluation methods consider the basic parameters of the transformer, operational data and other factors, but the evaluation criteria are greatly influenced by subjective factors, such as the experience of evaluating individuals and experts. Therefore, it is important to determine an evaluation method that is more in line with the actual operating conditions of the power distribution equipment, which can provide assistance for the state assessment of the distribution transformer, and have reference value for the economics of the power supply enterprise and the reliability of the power marketing.

In this paper, based on the large amount of operational information generated during the operation of the distribution network equipment, a state evaluation model of the distribution network equipment integrating multi-source information is established. The model comprehensively considers the critical state quantities of the distribution network equipment, and based on the fuzzy iterative method of big data and the establishment of the weight expert database, weights the multi-source information and reasonably evaluates the equipment status. Finally, taking the distribution transformer as an example, the evaluation results of the fusion of multi-source information proposed in this paper are proved to be more comprehensive. The method proposed in this paper can accurately judge the running status of the power distribution equipment based on various types of information, and provide a reference for the subsequent power marketing evaluation of the user equipment state, which is more instructive.

### **2. Feature Extraction and Scoring of Key State Quantities of Distribution Equipment**

During the operation of the distribution network equipment, a large number of data are generated, including real-time data, historical data, hardware information, environmental conditions, etc. Therefore, appropriate processing is required to extract key state quantities and establish reasonable evaluation criteria.

### *2.1. Selection of the State Quantity of a Distribution Transformer*

The state quantity of a distribution network device can directly or indirectly characterize various conditions during the operation of the equipment, and has guiding significance for the state evaluation of the distribution network equipment. At present, there are uniform standards and clear specifications in technology [30], as shown in Table 1.


### **Table 1.** Typical state quantity of a distribution transformer.

It can be seen from Table 1 that the state of the distribution transformer is large, and it is of grea<sup>t</sup> significance to reasonably select the state quantity and establish a scientific and comprehensive evaluation system for the state evaluation of the transformer. Since the distribution transformers used by industry and large users are mainly step-down transformers, and most of them are oil-immersed transformers, refer to the standards such as the State Network Distribution Equipment Status Evaluation Guidelines [31], according to the selection of key state quantities. The principle selects and classifies the state quantities of the distribution transformers in Table 1, as shown in Table 2.

> **Table 2.** Selection and classification of distribution transformer key state quantity.


### *2.2. Scoring Criteria for Key State Quantities of Distribution Transformers*

After the state quantity is selected, it needs to be scored to further evaluate the state of the distribution transformer. According to the unified regulations, the evaluation principles of each state quantity are shown in Table 3.


**Table 3.** Grading standard for distribution transformer status.

It can be seen from Table 3 that the state quantities of the transformer have both qualitative indicators and quantitative indicators of different orders of magnitude and dimensions, so the state quantities need to be normalized before evaluation. The state quantities, including winding DC resistance, oil temperature and other state quantities, which can make the state of the equipment better when become smaller or lower, are treated by Equation (1); the state quantities such as withstand voltage test, insulation resistance and other state quantities, which can make the state of the equipment better when it becomes more powerful and larger, is treated by Equation (2); for state quantities of qualitative measurements (running time, containment performance, etc.), the degree of deterioration is given empirically based on experience.

$$\mu\_{ij} = \begin{cases} 0 & \mu\_{ij} \le \mu\_{i\bar{j}0} \\ \frac{\mu\_{i\bar{j}} - \mu\_{i\bar{j}0}}{\mu\_{i\bar{j}1} - \mu\_{i\bar{j}0}} & \mu\_{i\bar{j}0} < \mu\_{i\bar{j}} \le \mu\_{i\bar{j}1} \\ 1 & \mu\_{i\bar{j}} > \mu\_{i\bar{j}1} \end{cases} \tag{1}$$

$$\mu\_{ij} = \begin{cases} 1 & \mu\_{ij} < \mu\_{i\mid 1} \\ \frac{\mu\_{ij0} - \mu\_{ij}}{\mu\_{ij0} - \mu\_{ij1}} & \mu\_{ij1} \le \mu\_{ij} < \mu\_{ij0} \\ 0 & \mu\_{ij} \ge \mu\_{i\mid 0} \end{cases} \tag{2}$$

where <sup>μ</sup>*ij*(*<sup>i</sup>* = 1, 2, ··· , 9) is the value of *j* is determined by the state quantity; *i* indicates the relative deterioration degree of the state quantity, and the value range is [0,1]; μ*ij* indicates the observation value; / indicates the ideal value or the factory value; μ*ij*1 indicates the attention value or the warning value. The value of μ*ij*0, μ*ij*1 refers to reference [32,33].

According to the state quantity evaluation criteria given in Table 3, with reference to [32,33], and combined with the experience of a large number of experts and long-term experience, the evaluation set of the key state quantities of the distribution transformer in Table 2 is shown in Table 4.



### **3. Weight Determination Based on Fuzzy Iteration and Expert Weighted Database**

After the key state quantity of the power distribution switch is selected, it is necessary to perform reasonable weight allocation for each state quantity to perform comprehensive evaluation of the state of the distribution network equipment. In this paper, we use the eclectic fuzzy decision-making and multi-level fuzzy comprehensive evaluation model to analyze the previous data of the distribution transformer; continuously update the weight ratio of the evaluation set through the weight inverse operation; reduce the influence of subjective factors brought by the expert review opinions; and improve the data, the reliability of the analysis and ultimately the establishment of a weight expert database.

### *3.1. Compromising Fuzzy Decision Weight Solving Process*

The flow chart of the compromise fuzzy decision [34] is shown in Figure 1. The basic principle is the virtual fuzzy positive ideal and the fuzzy negative ideal. Then, the Euclidean distance method is used to determine the distance between the candidate object and the fuzzy positive and negative ideals, and the membership degree belonging to the fuzzy positive ideal is calculated to determine the selection scheme. The greater the degree of membership, the better the solution and the priority.

**Figure 1.** A flow chart of eclectic fuzzy decision-making model.

The basic solution steps for the compromising fuzzy decision are as follows:

Step 1: The indicator data is transformed into a triangle fuzzy number representation. Let *F*(*R*) be the overall fuzzy set on *R*, set *M* ∈ *<sup>F</sup>*(*R*). The membership function μ*M* of *M* is expressed as

$$\mu\_M(x) = \begin{cases} \frac{x-l}{m-l}, x \in [l, m] \\ \frac{\frac{\mathcal{X}-\mathcal{U}}{m-\mathcal{U}}, x \in [m, \mu] \\ 0, x < l \text{ or } x > \mu \end{cases},\tag{3}$$

where *l* ≤ *m* ≤ *u*, and *M* is called a triangular fuzzy number, which is recorded as *M* = (*l*, *m*, *u*) = (*mL*, *m*, *mR*).

According to the Equation (3), the qualitative index, the quantitative index and the weight data in the state quantity are unified into a triangular fuzzy number.


$$
\mu\_i = (\mu\_i, \mu\_i, \mu\_i). \tag{4}
$$

After all the indicators are converted into triangular fuzzy numbers, the fuzzy indicator matrix is obtained and recorded as *F* = (*fij*)*m*×*n*.

3. The representation of the triangular fuzzy number of the weight vector. For the quantitative indicator, according to Equation (4), the triangular fuzzy number of its weight is expressed as follows:

$$w = [(w\_1, w\_1, w\_1), (w\_2, w\_2, w\_2), \dots, (w\_{\bar{i}i}, w\_{\bar{i}i}, w\_{\bar{i}})].\tag{5}$$

For the weight of qualitative indicators, use the transformation method of Table 5 to convert it into an expression of triangular fuzzy numbers.

**Table 5.** Triangular fuzzy number ratio method for transforming qualitative index into quantitative index.


Step 2: Normalize *F*. Suppose there are *N* evaluation objects, and the evaluation index *j*(*j* ∈ *N*) corresponds to *N* fuzzy index values in *F*, and is denoted as *xi* = (*ai*, *bi*, *ci*), (*i* = 1, 2, ··· , *<sup>N</sup>*). Then, the normalization equation of *xi* is as follows:

1. When *xi* is the fuzzy indicator value corresponding to the cost indicator, the normalization equation is:

$$y\_i = \left(\frac{\min(a\_i)}{c\_i}, \frac{\min(b\_i)}{b\_i}, \frac{\min(c\_i)}{a\_i} \wedge 1\right). \tag{6}$$

2. When *xi* is the fuzzy indicator value corresponding to the profitability indicator, the normalization equation is:

$$y\_i = \left(\frac{a\_i}{\max(c\_i)}, \frac{b\_i}{\max(b\_i)}, \frac{c\_i}{\max(a\_i)} \land 1\right). \tag{7}$$

The normalized fuzzy indicator matrix is recorded as *R* = (*yij*)*m*×*n*.

Step 3: Construct a fuzzy decision matrix D. The fuzzy decision matrix can be obtained by weighting R:

$$D = \left(r\_{ij}\right)\_{m \times n'} \tag{8}$$

where

$$r\_{ij} = w \oplus y\_{ij}(i = 1, 2, \cdots, N, j = 1, 2, \cdots, N) \tag{9}$$

Step 4: Determine the fuzzy positive ideal *M*<sup>+</sup> and the fuzzy negative ideal *M*<sup>−</sup>.Assume

$$\begin{array}{l} \mathcal{M}^{+} = (\mathcal{M}\_1^{+}, \mathcal{M}\_2^{+}, \dots, \mathcal{M}\_N^{+})\\ \mathcal{M}^{-} = (\mathcal{M}\_1^{-}, \mathcal{M}\_2^{-}, \dots, \mathcal{M}\_N^{-}) \end{array} \tag{10}$$

where *<sup>M</sup>*+*j* = max*<sup>r</sup>*1*j*,*r*2*j*, ···*rnj*(*<sup>j</sup>* = 1, 2, ··· , *N*) and *<sup>M</sup>*<sup>−</sup>*j* = max*<sup>r</sup>*1*j*,*r*2*j*, ···*rmj*(*<sup>j</sup>* = 1, 2, ··· , *N*) respectively represent the fuzzy maximum and minimum values corresponding to the fuzzy index of column *j* in the fuzzy decision matrix.

Step 5: Determine the distance *d*+*i*, *d*−*i*between the evaluated object *i* and *M*+, *M*<sup>−</sup>.

$$d\_i^+ = \sqrt{\sum\_{j=1}^N \left(r\_{ij} - \mathcal{M}\_j^+\right)^2}, i = 1, 2, \cdots, N. \tag{11}$$

$$d\_i^- = \sqrt{\sum\_{j=1}^N (r\_{ij} - \mathcal{M}\_j^-)^2}, i = 1, 2, \cdots, N. \tag{12}$$

Step 6: Fuzzy optimal decision making. Let the evaluation object *i* be subordinate to the fuzzy positive ideal membership degree as μ*i*, and then fuzzy optimal decision making. Let μ*i* be the membership degree that the evaluation object *i* subordinate to fuzzy positive ideal; then

$$\mu\_{i} = \frac{d\_{i}^{-}}{d\_{i}^{+} + d\_{i}^{-}}, i = 1, 2, \cdots, N. \tag{13}$$

Obviously 0 ≤ μ*i* ≤ 1, if *Ai* is closer to *M*+, the closer μ*i* is to 1. The classification results of the membership degree are used to sort the pros and cons of the sample and form a fuzzy expert group commentary set of the multi-level fuzzy comprehensive evaluation model.

### *3.2. Multi-level Fuzzy Comprehensive Evaluation Model*

In order to reduce the influence of subjective factors caused by expert experience and avoid errors caused by data redundancy or errors or omissions, this paper adopts a combination of eclectic fuzzy decision-making and multi-level fuzzy comprehensive evaluation to improve the evaluation accuracy of distribution transformer state assessment. The specific steps of the model are as follows:

Step 1: Determine the set of objects to be evaluated *X*{*<sup>x</sup>*1,*x*2, *x*3, ··· , *xk*}; determining factor set *U* = {*<sup>u</sup>*1, *u*2, ··· , *un*}; confirm the comment set *V* = {*<sup>v</sup>*1, *v*2, ··· , *vn*}.

Step 2: According to the factor set *U* and the comment set *V*, the evaluation matrix *Ri* is obtained.

$$R\_i = \left\{ \begin{array}{cccc} r\_{11}^{(i)} & r\_{12}^{(i)} & \cdots & r\_{1m}^{(i)} \\ \vdots & \vdots & & \vdots \\ r\_{n1}^{(i)} & r\_{n1}^{(i)} & \cdots & r\_{n1m}^{(i)} \end{array} \right\}. \tag{14}$$

Step 3: Make a comprehensive decision for each *Ui*. Let the weight of *Ui* be assigned as *Ai* = *a*(*i*) 1 , *a*(*i*) 2 , ··· , *a*(*i*) *ni* , and *ni i*=1 *a*(*i*) *i* = 1. If *Ri* is a one-factor matrix, then the first-level evaluation vector is obtained as follows

$$A\_i \times R\_i = (b\_{i1}, b\_{i2}, \dots, b\_{in}) \Delta B\_i, \ i = 1, 2, \dots, s. \tag{15}$$

Step 4: Think of each *Ui* as a factor, so *U* is a single factor set, and the single factor judgment matrix of *U* is:

$$R = \begin{pmatrix} B\_1 \\ B\_2 \\ \vdots \\ B\_s \end{pmatrix} = \begin{pmatrix} b\_{11} & b\_{12} & \cdots & b\_{1m} \\ \vdots & \vdots & & \vdots \\ b\_{s1} & b\_{s2} & \cdots & b\_{sm} \end{pmatrix} \tag{16}$$

Each *Ui* is considered part of *U*, reflecting a certain attribute of *U*, which can be weighted according to their importance.

$$A = (a\_1, a\_2, \dots, a\_\kappa). \tag{17}$$

The second-level fuzzy comprehensive evaluation model is obtained as follows:

$$B = A \times R = (b\_1, b\_2, \dots, b\_m). \tag{18}$$

If there are more factors in each sub-factor *Ui* = (*i* = 1, 2, ··· ,*<sup>s</sup>*) you can continue to divide *Ui*.

Step 5: After obtaining the weight distribution, replace it with Step 3 in the basic solution step of the compromise fuzzy decision, that is, the establishment of the fuzzy weight, and then obtain the final computer expert library through repeated iterations. This not only gives a review of the computer expert library for the new data, but also expands the sample data for the computer expert library.
